What is the purpose of two-point problem in plane table survey? Explain the process of two-point problem?
What do you understand by two-point problem? Explain how it is performed in field.
Two-Point Problem in Plane Table Survey: In the two point problem survey, the plane table is observed, measured and located from two well defined known points. Whose measurement is already taken by Plane Table Survey.
The following procedure IS used:
- Choose a suitable auxiliary station D near C so that the angles CAD and CBD are neither two acute nor two obtuse. Set up the plane table at D. Level it. Orient the table approximately using a magnetic compass of alternatively, be eye-judgement. Thus the line ab is made approximately parallel to AB. Clamp the plane table (Fig).
- Pivot the alidade on a and sight A. Draw a ray through a. Similarly, pivot the alidade on b and sight B. Draw a ray through b, intersecting the ray through a at d1.
The point d1, gives the approximate position of the ground point D, because the orientation at D is approximate. Transfer the point dl to the ground using a plumbing fork and drive a peg. 3. With the alidade pivoted at d], sight the station C. Draw a ray d 01 to represent the distance DC. Mark the position of C1 by estimation.
- Shift the plane table to C and centre it so than the point 01 is above C. Orient the plane table by Back-sighting on D. Thus the orientation at C is the same as it was at D.
- Pivot the alidade against a and sight A. Draw a ray ac2 to intersect the ray dlc1 produced at c2. Thus 02 represents the approximate position of the point C, because the orientation is still approximate. The point b1 gives the approximate position of B with respect to the orientation made at D.
As the length ab is the true representation of AB, the error in the orientation is equal to the angle b1 ab between the lines ab and abl.
- To eliminate the error in the orientation, place the alidade along abl. Fix ranging rod at a point P at some distance from the plane table and in lien with ab].
- Place the alidade along ab and turn the plane until the ranging rod at P is bisected. Clamp the plane table. Now the orientation of the plane table is correct and the lien ab is exactly parallel to AB.
- To find the true position c of the station C, centre the alidade on a and sight A. Draw a ray ca through a (not shown).
Similarly, centre the alidade on b and sight B. Draw a ray cb through b. The intersection of the ray’s ca and cb gives the true position of c (not shown).
Unless the point P is chosen quite far off from C, it becomes difficult to orient the plane table at C correctly. As the distance of P from C is generally limited due to other considerations, two-point problem does not give accurate results.
Moreover, more work is involved in a two-point problem than in a three-point problem as the table has to be set up at two stations.